A2 = A-vertex of second Brocard triangle (singular focus)
foot Ha of A-altitude
point at infinity of median AG
We meet these three curves in "Orthocorrespondence and Orthopivotal Cubics" §6.5.1. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary.
O(A) = K053-A (figure above) is :
O(B) = K053-B and O(C) = K053-C have analogous properties obtained by cyclic permutations.
The isotomic conjugation transforms O(A), O(B), O(C) into three concentric hyperbolas passing through X(298) and X(299), with center X(325) = isotomic conjugate of the Tarry point X(98).
See also Paul Yiu's paper "Conic Construction of a Triangle from the Feet of Its Angle Bisectors" here.